Momentum calculator
Multiply mass by velocity and get linear momentum with its sign: 2 kg moving at 5 m/s carries 10 kg·m/s, and a reversed velocity gives a negative result, so opposite motions can cancel. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Mass m in kilograms
- 2
- Velocity
- 5
- Momentum
- 10
- Magnitude
- 10
- Direction
- positive
Linear momentum is the product of a body's mass and its velocity. In one dimension the defining relation is simply p equals m times v. When mass is measured in kilograms and velocity in metres per second, momentum is reported in kilogram metres per second, the SI unit for linear momentum. Unlike kinetic energy, which is always non-negative and quadratic in speed, momentum keeps the sign of the velocity, so two equal masses moving in opposite directions can cancel each other in a collision analysis. Students, teachers, robotics engineers, and game developers use this one-line formula constantly for homework checks, collision prep, and first-pass conservation arguments. This calculator accepts mass and velocity, returns signed momentum, magnitude, and direction, and rejects non-numeric or non-finite inputs with a clear validation error instead of producing NaN.
How linear momentum is defined and computed
Begin with a one-dimensional axis and choose a positive direction. Mass m is a non-negative scalar in everyday mechanics, though this calculator accepts any finite number so that symbolic or signed mass conventions in advanced models are not silently rewritten. Velocity v is the rate of change of position along the chosen axis; it may be positive, negative, or zero.
Linear momentum is defined as the product p equals m times v. That single product is the quantity that is conserved for an isolated system in the absence of external forces, and it appears as the first moment of the mass distribution in continuum mechanics. When velocity is zero, momentum is zero regardless of mass.
When mass is zero, momentum is zero regardless of velocity in the non-relativistic particle model used here. The SI unit of momentum is the kilogram metre per second, often written kg·m/s or N·s because impulse equals change in momentum. Both fields must be finite; NaN and Infinity are rejected with invalid input so clients can fix units and types rather than guessing.
Non-numeric strings such as words or empty tokens fail the same way. This page is intentionally limited to the closed-form product; angular momentum, relativistic four-momentum, and multi-body collision solvers are separate search intents and separate landings.
What you send and what you get back
Send two required finite numbers under the fields mass and velocity. Mass is typically in kilograms; velocity is in metres per second and may be signed so that reverse motion yields negative momentum. Classic textbook checks include two kilograms times five metres per second for ten kilogram metres per second, a negative velocity for reverse motion, and zero velocity for a body at rest.
Keep units consistent across a multi-step lab: if you measure mass in grams you must convert to kilograms before calling, or scale the result accordingly after, so the numeric product still matches the SI interpretation your report claims.
Where momentum calculators show up in real work
Secondary-school and introductory university physics courses assign mass-times-velocity drills, compare momentum with kinetic energy, and require signed results on a number line before conservation problems; a single trusted oracle speeds grading and demo setup. Sports science and biomechanics staff convert body-segment mass and impact velocity into linear momentum estimates for protective equipment studies without re-deriving units each session. Game engines and interactive simulations often need a closed-form momentum product for inviscid collision stubs and teaching demos where a full rigid-body solver is overkill.
If you later need impulse from force and time, elastic or inelastic collision outcomes, angular momentum of a rigid body, or relativistic momentum, treat those as separate search intents and landings rather than overloading this linear momentum calculator page.
What you can do with it
Homework and lab answer keys
Compute signed linear momentum p=mv from mass and velocity so students and auto-graders share one closed-form ground truth in kg·m/s.
Collision prep and conservation checks
Build before-and-after momentum tables for one-dimensional collision labs without manual unit mistakes.
FAQ
What formula does this momentum calculator use?
Linear momentum p = m × v, where m is mass and v is velocity. The result is reported in kilogram metres per second (kg·m/s) when mass is in kg and velocity in m/s.
What happens if mass or velocity is not a number?
Both fields must be finite numbers; missing fields, non-numeric strings, NaN, and Infinity are rejected and are not charged.
Can velocity be negative?
Yes. Velocity is signed along your chosen axis. Negative velocity produces negative momentum, which is essential for one-dimensional collision and conservation problems.
Is this the same as kinetic energy?
No. Kinetic energy is (1/2)mv² and is always non-negative. Momentum is mv and keeps the sign of velocity. They answer different questions and should stay on separate landings.
What does it cost?
The browser tool is free and runs locally.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/mech/momentum \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"mass":2,"velocity":5}'const res = await fetch("https://api.kit.forhosting.com/mech/momentum", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"mass": 2,
"velocity": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/momentum",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"mass": 2,
"velocity": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/momentum", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"mass":2,"velocity":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"mass":2,"velocity":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/momentum", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"mass": 2,
"velocity": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.momentum",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
How linear momentum is defined and computed
The entire pipeline is deterministic floating-point arithmetic: no random seeds, no wall-clock timestamps, no network calls, and no model drift, so identical inputs always produce identical JSON.
What you send and what you get back
Missing fields, non-numeric strings, NaN, and Infinity fail with invalid_input and are not charged. On success the response echoes cleaned mass and velocity, momentum as the primary SI product m times v, magnitude as the absolute value for tables that drop the sign, direction as positive, negative, or zero, a units hint object naming kg, m/s, and kg·m/s, method set to linear_momentum_mass_times_velocity, and the short formula string p equals m times v for display. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where momentum calculators show up in real work
Robotics and control labs report command momentum along a rail or conveyor from payload mass and encoder-derived velocity as a first filter before full dynamics models. Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Integration use cases
Robotics and payload momentum estimates
Estimate command linear momentum from payload mass and axis velocity before full multi-body dynamics models.